Question

A triangular prism is formed by planes whose equation are ay=bx y=0 and x=0 . find the volume of the prism between the planes z=0 and z=c+xy​

Answer 1

Answer:

a regular triangular prism is 5cm height,the perimeter of the base which is an equilateral triangle is 2cm. find the volume of the prism

Answer 2

Answer:

The volume of the prism between the planes z=0 and z=c+xy​ :  V = (1/6) $b^2$ π $a^{-1$c

Step-by-step explanation:

From the above question,

A triangular prism is formed by planes whose equation are ay=bx y=0 and x=0 .

Here we need to find the volume of the prism between the planes z=0 and z=c+xy​

                x = r cos(θ)

                y = r sin(θ)

The limits of the integration are :

                 r = zero to r = b and

                 θ = 0 to θ = π/2.

The region aspect in polar coordinates is dA = r dr dθ.

Therefore,

we have:

                V = (1/2) $b^2$/a (cπ/2 + (1/3) $b^2$/2)

Therefore, the extent of the triangular prism between the planes z=0 and z=c + xy is:

                V = (1/6) $b^2$ π $a^{-1$c

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